Volumetric parametrization from a level set boundary representation with PHT-splines. (January 2017)

• Record Type: Journal Article
• Authors: Chan, Chiu Ling; Anitescu, Cosmin; Rabczuk, Timon
• Is Part Of: Computer aided design. Volume 82(2017)
• Page Start: 29
• Page End: 41
• Publication Date: 2017-01
• Subjects: Volumetric parametrization -- Boundary representation -- PHT-splines -- Level set method; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2016.08.008
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a spline-based representation of a domain of interest from voxel-based data. We show an efficient way to obtain a boundary representation of the domain by a level-set function. Then, we use the geometric information from the boundary (the normal vectors and curvature) to construct a matching C 1 representation with hierarchical cubic splines. The approximation is done by a single template and linear transformations (scaling, translations and rotations) without the need for solving an optimization problem. We illustrate our method with several examples in two and three dimensions, and show good performance on some standard benchmark test problems. Highlights: A fast and automated method is proposed to get a spline-based model from voxel data. A hierarchical basis of C 1 cubic polynomials provides the volumetric parametrization. The shape of the boundary is approximated using a simple template in 2D and 3D. Complex domains with voids can be handled in a single-patch framework.